Two Open Questions from Today’s Twitter Tirade

If you want to start at the top, you’d start with this article and this tweet:

Loads of folks chimed in either to agree with me or to hassle me over my premises and I was grateful for both, but especially for the latter group which helped me sharpen up my argument.

I left with two open questions:

How do we decide whether to include a course as a university requirement for general education?

I agree that university students should take courses outside their major in order to develop balance, roundedness, and an appreciation for the diversity of humanity’s intellectual achievements — whether or not they’ll ever use those courses in their eventual profession.

Clearly, I don’t think Intermediate Algebra should be one of those required courses.

But how do we decide? You’re selected to represent all of mathematics and to advance a list of courses in which every student on campus will have to enroll.

How do you decide?

My initial criteria:

  • Would the course increase the odds that an undeclared student would want to major in the discipline?
  • Even if she didn’t major in the discipline, would the course encourage her to recommend it to underclassmen or her own children later in life?
  • Would she see it as a Jeopardy! category later in life and think, “Oh yeah, I can do some damage here.”


What kind of disciplinary knowledge should we expect of principals?

Someone wrote in to say that she was required to pass Intermediate Algebra as a prerequisite for becoming a principalship.

Is that threshold too high? Does it exclude too many effective principals?

Should we expect principals to be able to pass the final exam of any course offered on their campuses? Should they be able to score a passing grade on any Advanced Placement exam?

How do we decide?


  1. Russel Johnson

    July 1, 2017 - 6:20 pm -

    To me, what is important about a lot of the mathematics I teach/taught (moving to CS) is the logic and reasoning, paired with problem solving. I don’t know what that looks like on every level as far as courses go but it seems to have a home in mathematics for the time being.

    Also, anyone who has observed me is giving more pedagogical feedback than content. It seems to be understood that teachers should develop professional communities within our school and elsewhere for content-based feedback. Surely we can’t expect Admins to be fluent in all subject matter! (Easy to say for big content areas, but what about your outlier classes like Career Tech, foreign languages.

    Side note: I was math major in college and masters in secondary math ed. I was required to take 2 courses of foreign language as part of math undergrad (not to mention 4 English and 2 history courses). Perhaps universities and community colleges are going for a better “student” who helps represent the school well and at least has a foundational “understanding” (exposure really though) of all content areas.

    • Side note: I was math major in college and masters in secondary math ed. I was required to take 2 courses of foreign language as part of math undergrad (not to mention 4 English and 2 history courses). Perhaps universities and community colleges are going for a better “student” who helps represent the school well and at least has a foundational “understanding” (exposure really though) of all content areas.

      Yeah, I really have no dispute with all those extra GE requirements. I enjoyed my survey courses in history and my intro to comp in English. They left me encouraged to take more classes if I had more units to spare and I’d recommend them to underclassmen and my own kids.

      I’m only wondering: what are the math courses that’ll have the same results?

  2. Reply

    I don’t want to get into specifics in a public forum but I do know of a situation where lack of subject knowledge was an major issue.

    I think the key was the person *thought* they knew and did not trust the teachers when they explained why something was a bad idea.

  3. Reply

    I think this is almost a specifically US issue with its ideals that a university education provides a broad base combined with the fact that there is, to a large extent, no national curriculum, so we cannot necessarily count on students having already engaged with a variety of disciplines at a high level.

    In the Netherlands, it is assumed that high school has provided a broad base and that university is where students specialize. Therefore, if you wanted to major in communications or European studies, there is no need for you to take a math or science course; you have completed that in high school and now will focus on your specific field. All the courses that you take will be of special interest to your field.

    There are benefits and drawbacks to this approach. An obvious benefit is that no one who is not majoring in a technical field ever has to factorize a polynomial again after high school. A drawback is that you have to decide at a relatively young age what you want to specialize in, without the benefit of dabbling in lots of different courses or beginning as an “undeclared” major. (That being said, the cost of university is much lower here, so it is not uncommon for students to drop their major and reenroll with a different major.)

    • Super interesting comparison, Kate. In particular, I hadn’t thought about the low switching cost. Thanks for sharing.

  4. Reply

    Questions like this don’t open math up and expose people to the richness and value of it. They do the opposite. They aren’t checking for reasoning and thoughtfulness and problem solving, they’re checking for how well a student can monkey see monkey do. In that sense they harm not only struggling students, but bright students who succeed in courses but don’t see the value of math to enrich their lives.

    My main complaint is not that math classes are required, even algebra classes (although they would not be tops of my list), but HOW they are taught. Rational expressions can either be something learned by wrote and with rules, or they can be a great way to explore rates of growth and how types of growth combine and work with or against each other. Which is more valuable? Which makes people think math is important and worth learning? ESPECIALLY for future school leaders it would be wonderful for them to be exposed to the value and richness if math, but how often are required math classes doing that vs the opposite?

  5. Reply

    … I personally don’t care if my principal knows my subject – provided, of course, that they know enough of it to do the job of running the school effectively.

    Love this distinction.

    What I DO care about is that they aren’t scared of my subject. I’m sick of people talking about how they don’t ‘do’ math, or contributing to our cultural hate/fear of math. Part of the principal’s job is to establish and maintain a school culture of learning and acceptance of all subjects. (And, gold star if they can get to a love of all subjects!)

    If I, as a math teacher, am required to be familiar with – and teaching – English language standards, what is so wrong with English teachers being required to be familiar with and teaching math standards? If it is unacceptable for me to say ‘Well, I just don’t do English’, then why is it so common for English teachers to not ‘do’ Math?

    (For the record, I do also incorporate and teach English standards as they are relevant to my students and the math content. Also, I have a unicorn principal… Former English teacher with a love of mathematics, and a good understanding of how administration should work!)

  6. Reply

    I guess the question is this: if college doesn’t need math beyond algebra, then why does the job need college?

    Most of the students attending college have taken math through algebra 2. I know this because I teach a lot of them. My goal for seniors in algebra 2 is that worst case, they’ll be in a year of remedial math.

    So if you don’t want them demonstrating knowledge of algebra 2 material in college, then why should they need college? Why not just let employers hire them directly out of high school?

    By the way: California, Tennessee, and New York are ending remedial education (, so now people who can’t demonstrate middle school level understanding of math will be getting college credit for taking middle school math courses–in schools that require algebra 2 on the transcript. At what point will we stop lying?

    • It’s not a trick question. College isn’t trade school. A college diploma, originally, meant graduates have a certain level of advanced knowledge. If you just need a little bit of nursing training, take a certificate. If you want a BS in Nursing then you should have some level of math ability–or stop calling it a BS. A principal usually has to get a Master’s degree. Is it unreasonable to ask that someone have basic math capability, the same math they’d need to get a decent SAT score, if they’re going to get a Master’s degree?

      Our entire high school math program is premised on the fact that kids should get as far as they can in math in order to get success in college. Now some colleges are allowing students to get college credit for middle school math, while others are getting castigated for making a college diploma mean something.

      If you’re going to argue that college needs no high school math, then why not start pushing for high schools to be able to teach low level math? Right now, most high school students aren’t allowed to take anything lower than pre-algebra, If colleges are allowed to say “oh, who needs this? She’s just going to be a nurse. Let’s give her a college diploma and hope no one notices she couldn’t pass a high school algebra class”, then why aren’t high schools allowed to say “look, half our kids don’t know middle school math. Can we stop pretending to teach them advanced math and give them a better grounding in fractions and ratios?”

      Moreover, isn’t your point that good teachers can engage and get any students to learn? And haven’t you, in the past, pushed back on teachers who argue that no, some of this math is too hard for the students, that they need either interest or ability? Why isn’t it the job of college professors and the older students, responsible for their own decisions, to learn enough math to justify a college diploma?

      Most students take algebra 2 in high school. Most college students can’t demonstrate algebra 2 ability in college. Generally, it has been agreed up to this point that ability to do advanced math is a key requirement for a college degree.

      So it seems to me that people who get angry at the very idea that advanced math is reasonable for college ought to be pushing for much lower high school math requirements. Because far more kids are being shoved into math classes they don’t want, then shoved into summer school to offer seat time for a passing grade, and I don’t see people getting upset about that.

    • A college diploma, originally, meant graduates have a certain level of advanced knowledge.

      Agreed. More for some majors than others. A general level of advanced knowledge for all a/k/a general education.

      But throughout your comment, you assume the definition of “advanced knowledge” should be “the punishing and pointless symbolic manipulation of Algebra 2.” That currently is the definition, but it should be revised as soon as possible.

      A BS / HS diploma should require a foreign language. It shouldn’t be Latin.

      A BS / HS diploma should require some literature. It shouldn’t be the installation manual for a rotary telephone.

      A BS / HS diploma should require some history. It shouldn’t be a semester-long course analyzing the Tariff of 1824.


  7. Reply

    Other than tradition, I’ve always wondered what’s the big deal about Algebra 2 content? I’m currently working through two courses on, both of which have parts that are kicking my Algebra 2 Proficient butt: “Outside the Box Geometry” and “Algebra Through Puzzles.” Neither require Algebra 2 knowledge and, in fact, both require little more algorithmic knowledge than what’s taught in an 8th grade algebra or a basic geometry course. So either we, as a society, really value the content of Algebra 2 (which I highly doubt), or we deem it a measure of one’s smartness. If our goal is something more powerful, such as that high school graduates should be able to reason and solve complex problems, then this opens up far more options of what the content could be of graduation required math courses.

  8. Reply

    The application of the content basics to the post-secondary choice of professions or trades is of the utmost importance. Along with application comes the necessity for problem-solving, and mathematics lends itself very well to that in school as well as life in the “real” world. The processes and the tools can be made relevant at any level of education or any walk of life.

Leave a Reply

Your email address will not be published. Required fields are marked *